On the bi-Hamiltonian structure, dressing transformation and constrained flows for equations in (2 + 1) dimensions

We have shown that nonlinear equations in (2 + 1) dimensions which are completely integrable can be analysed on the basis of an operator which is the analogue of the pseudo-differential operator for the discrete case. The bi-Hamiltonian structures of such equations are derived and an analogue of the Sato equation is seen to hold, which can be used to construct multi soliton solutions via Casorati determinants, in the case of the periodic boundary condition. Lastly the constrained flows are constructed.